A five year bond has a par value of $1000, and annual coupon of 3 percent, and a price of $957.

(a) Calculate the yield to maturity of the bond

(b) Calculate the modified duration of the bond

(c) Using the duration expression deltaP/P = -D * deltay (where P is the price, D is the modified duration, and y is the yield to maturity), graph the percentage change in price as a change in yield to maturity

(d) Calculate the actual change in price as a function of the change in yields and graph the two functions on the same graph, using the fact that P = PV

(e) Calculate the convexity of the bond

(f) On the same graph, now graph the estimated percentage change in price with the convexity adjustment: deltaP/P = -D * deltay + (1/2) Convexity * (deltay)^2